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Emily is twice as old as Charlotte. Four years ago, the product of their ages was 30. Use a quadratic equation to find Charlotte's present age.

 

First I said E (Emily) = 2C (Charlotte) 

Then . . .

 

(E-4)*(C-4)=30

EC-4E-4C+16=30

EC-4E-4C=14

EC-4E-4C-14=0

 

Next I substituted in [E=2C]

(2C*C)-(2C*4)-4C-14=0

2C^2-8C-4C-14=0

2C^2-12C-14=0

 

Then I factorised . . .

2*(C^2-6C-7)=0

2*(C-7)*(C+1)=0

 

So Charlotte's present age must be 7.

 

To check it . . .

E=2*7=14

(E-4)*(C-4)=30

(14-4)*(7-4)=30

10*3=30

 

I thought this might interest at least one person.

zacismyname  May 3, 2015

Best Answer 

 #2
avatar+981 
+5

Nice 

I didn't think of doing it like that. The more direct route for sure.

zacismyname  May 3, 2015
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2+0 Answers

 #1
avatar+78577 
+5

Very nice, zacismyname   !!!   ....you're correct.....this is a good one  !!!

We could also do it with one varable from the start :

Let Charlotte's age be x  and Emily's age be 2x

So we have

(2x - 4)(x - 4) = 30

2x^2 - 12x + 16 = 30

2x^2 - 12x - 14 = 0

x^2 - 6x - 7  = 0

(x - 7) (x + 1) = 0      so x = 7 or  x = -1   .....reject  - 1  .....

So.....x = 7  = Charlotte's age     and 2(7)  = 14 = Emily's age

Just as you found  !!!!

 

  

CPhill  May 3, 2015
 #2
avatar+981 
+5
Best Answer

Nice 

I didn't think of doing it like that. The more direct route for sure.

zacismyname  May 3, 2015

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